For the Aristotelian Society Supplementary Volune 1998

DRAFT

Transcendental Tense

D.H Mellor and J.R. Lucas

II-----J.R. Lucas

Professor Mellor holds to a tenseless account of time,
and would encourage those of us who do not, to recognise
how it can make better sense of some of Kant's dark
sayings, suitably re-interpreted, than Kant himself
could. Kant was a projectivist, holding that temporal
terms were imposed by us on the world rather than
discovered by us in the world. Mellor subscribes to real
time, construes tense as a perspective that we, as
agents, have to adopt, but not corresponding to anything
in the fabric of the universe. Some of Kant's arguments
for the unreality of time have already been invalidated
by a deeper understanding of the issues involved and by
the development of the General Theory of Relativity, but
the arguments of the First Antinomy involve a tensed
theory of time, and can be parried, Mellor hopes, by
showing that it is tense, not time itself, that gives
rise to the contradiction.

Kant's First Antinomy can be made intelligible by
topology, and was refuted by Aristotle. Besides the
distinction between tensed and tenseless temporal
predicates (McTaggart's A series and B series) adduced by
Mellor, we need two further distinctions, the distinction
between instant and interval and that between metric
infinity and topological openness. Advocates of a
dynamic theory of time tend to talk of a process, the
passage of time, which must occupy an interval---often
the ``specious present''. On this account, the adjective
`present', like `past' and `future', characterizes an
interval, an interval of indeterminate duration, often
varying with context---``the present week'', ``the
present government'' the `present century''. But under
Augustinian pressure the present interval can be made to
shrink and shrink and shrink until in the limit it
becomes a punctiform instant, with the instantaneous
present `now' being the boundary between the past
interval and the future interval, both distinguishing
them as separate temporal regions and uniting them into a
single whole of time.

If we take `the present' as meaning `the present
interval', then the first half sentence of Kant's
Antithesis is true. The world has no beginning. But it
does not follow that it is metrically infinite. For
although the present interval cannot be of zero duration,
there is no minimum duration required for it to be an
interval in which processes can take place. Around the
time of the Big Bang things happened very fast. All that
can be established is that if time is constituted by a
continuous process of becoming, with the present being a
topologically open interval, then time, being an infinite
union of open intervals, is itself open. (It does not
immediately follow that it could not be closed too, but
it is reasonable in the context of Kant's argument to
reckon that it could not have a boundary, a first
instant.)

Tense theorists who construe `the present' as
referring to the present instant run into lesser
problems. It might be claimed that even if only an
instant was being referred to, an interval was implicit
in the characterisation; after all, in the differential
calculus, although we ascribe differentials at a point,
we define them in terms of a sequence of intervals. In
order to make the charge stick at the very beginning of
time, we might amend the standard account of a
differential as the limit, as dt tends to zero, of
[f(t+dt) - f(t)]/dt, and define a fluxion more
symmetrically as the limit, as dt tends to zero, of
[f(t+dt) - f(t - dt)]/2dt. In that case the protagonists
of the instantaneous present would be embarrassed by a
beginning of time, as they would be, even with the
standard differential, by an end of time. But the
embarrassment need not last long. By any reckoning the
beginning and end of time are exceptional, singularities
for which a special account may need to be given. It is
not a serious criticism of the Dedekind cut that for the
number 0 it does not divide the positive rational numbers
into two classes, but is merely the lower limit of the
whole class. Equally if we took an Cantorian approach,
the fact that for 0 we did not have nested intervals, but
only half-nested ones would not worry us unduly, and by
the same token a protagonist of the present interval
could maintain that the temporality of intervals at the
beginning of time was sufficiently secured by what
followed them, even though, in their case, they had no
antecedents.

The other half of the First Antimony was shown to be
invalid by Aristotle's argument of the dichotomy. Before
the runner can arrive, he must get half-way there; before
the runner can get half-way there, he must get half way
to being half-way there; before the runner can get half
way to being half-way there, he must get half way to that
position. . . and so on; . We have an infinite series
of instants, of order-type w* (omega superscript star)
the order-type of the negative integers, which must
precede any conclusion of a process. There may be
practical difficulties in completing a series with w* of
separate tasks---Wittgenstein said he would be surprised
to meet someone who had just counted down from minus
infinity to zero---but there is no difficulty in allowing
conceptually that an infinite series of instants precedes
a particular instant. Indeed, it is not only instants,
of measure zero, that can precede a particular instant,
but intervals, possessing non-infinitesimal temporal
magnitudes as well. Hoyle's theory of continuous
creation, which posited the universe having existed for
always, was coherent and widely held, until the echoes of
the Big Bang told empirically against it.

Kant's difficulties with time are not due to its being
tensed. But Mellor commends his tenseless view on other
grounds too, as avoiding McTaggart's conclusion that the
flow of time entails a contradiction, and as being in
accord with the Special Theory of Relativity. As a loyal
Cambridge man, Mellor accepts McTaggart's argument that
ascriptions of tense inevitably involve a contradiction,
since events are at one time future, then present, then
past, but cannot be both future and present and past. To
this the obvious retort is that these ascriptions of
futurity, presentness and pastness are made at different
times, so that no contradiction is involved, any more
than if I was at Winchester, am at Cambridge, and shall
be at Oxford. But that retort is thought to be naive.
My writing this paper was future, is present and will be
past, true: but, it is said, these complex tenses
likewise involve a contradiction, in as much as each
event has to have incompatible complex tenses. Once
again the same retort is made, that the incompatible
ascriptions are made at different dates, so that no
contradiction is generated, and once again the resolution
is reconstrued in terms of yet more complex tenses,
themselves said to give rise to a further contradiction.
The critics of tense claim this as a victory, and that
they have discovered an vicious regress in the concept of
tense: but it does not look like that to their opponents,
who accuse them of being needlessly muddled at each
stage, and when their muddle is pointed out to them,
deliberately getting further muddled about the reply. In
such a stand-off it is clear that deeper issues are at
stake, and that the two parties are being moved by
metaphysical assumptions which we need to make explicit.

Mellor, recognising that McTaggart's argument may not
convince, offers a further one based on token-reflexives
(or indexicals).1
Tenses are essentially token-reflexive.
The present tense is used of events
contemporary with the time of speaking, the past of
events that happened before the time of speaking, and the
future of events expected to take place after the time of
speaking. No exclusively non-token-reflexive
translations of tensed utterances can be given,
nor can their truth conditions be expressed in exclusively non-token-reflexive terms.
Rather, the truth conditions of
tensed utterances are functions of the time of their
utterance as well as the tenseless facts of the case.
And so, Mellor concludes, tense is unreal.
But it does not follow. The argument does not show that tensed
language is inherently self-contradictory, only that it
is token-reflexive. Further argument is needed to show
that it is bad. Plato would give it. Token-reflexives
were bad, for the reason that Russell's term,
``egocentric particulars", suggests: they depend on the
self, when I speak, where I am situated, who I am. And
Plato was against the self. The self was arbitrary,
fickle and unreliable, making judgements based on
immediate inclination rather than rational consideration.
The philosopher, therefore, should disengage himself from
the transitory flux of the here and now, and be a
spectator of all time.2

Nevertheless, Mellor concedes a lot to tense. There
are tensed propositions, whose truth-value varies with
time: these tensed propositions, though not equivalent to
tenseless ones, are essential for agents' being able to
act effectively. Nevertheless, since the truth-
conditions of tensed propositions can be expressed
tenselessly, time itself must be tenseless too. But why?
It is allowed that something is being left out as regards
meaning. Why are truth-conditions all-important, and
meaning of no significance? It seems that `real' is
being glossed in an extremely Platonic sense. Mellor
would have the philosopher able to account for agents'
being able to take timely and effective action, but not
be himself an agent needing to know what o'clock it was,
and whether it was time to give a lecture or attend a
college meeting. Such a stance is always possible, and
sometimes desirable; but not universally obligatory. It
leaves out too much, and has a defective view of what it
is to be a person. Ego ergo ago. We are not just
ratiocinating observers, taking a God's-eye view from
nowhere, but agents whose knowledge comes from
interacting with the world. Conditions for effective
agency, therefore, are conditions for acquiring
knowledge, and not to be downgraded as somehow failing to
be real. Moreover, tenses are not so much egocentric as
nos-centric. I talk to you, and use the present of what
is happening when you are listening, the past of what
happened before, and the future of what will happen after
our conversation. It is not the arbitrary choice of my
selfish self, but the necessary framework of our
dialogue, in which you and I communicate with each other,
pool information and share rationality. Even Plato
should concede reality to tense on the score of
dialectical necessity.

Extreme non-token-reflexive accounts of reality are
defective. A tenseless account of time is likely to be
as little use as a map which does not enable us to locate
on it where we are, or a list of guests at a party with
no means of discovering to whom one is talking. Language
needs to conjugate over tenses as it needs to conjugate
over the first- and second-persons. Otherwise it has no
anchor in experience, and fails to address us in our
actual situation. And yet, it may be argued, we do have
a third-personal language purged of token-reflexive
terms: scientists affect such an impersonal language, and
it clearly succeeds in communicating information. In
what sense, then, is it defective? There are two answers:
first, that it is parasitic on ordinary language for its
meaning, and second that it depends on some token-
reflexive term to secure its reference, and hence its
statements being able to be true or false. The first
answer allows that a language without token-reflexives is
used and understood, but claims that it is understood
only because we are able to give content to terms such as
`earlier' and `later' from our antecedent understanding
of words such as `yesterday' and `tomorrow', `ago' and
`soon'. Novels are read and understood, even though
containing no genuine token-reflexives, but we understand
what the third-personal descriptions mean because we
already know from our ordinary discourse what first- and
second-personal terms mean. Admittedly, it is difficult
to show that people could not come to understand
something unless some favoured condition were satisfied.
Mathematicians can characterize space in abstract terms
without any apparent reliance on spatial experience. In
his book Mellor argues that time can be explicated in
terms of causality, itself distinguished from spurious
cases by the condition of near-contiguity. But that
condition is at best a contingent one: action at a
distance, whether spatial or temporal, is conceivable,
and has been actually accepted as true. In any case, the
concept of causality is acquired, I believe, through our
being agents, so that the explication is not, ultimately,
totally non-token-reflexive. Moreover, although Mellor's
exegesis of the conceptual links between time and other
fundamental categories is illuminating, we often draw on
an antecedent concept of time in interpreting our
abstract formulations. When I do old-fashioned physics,
and locate events in R3 X R, I understand the latter not
as a mere dimension, but as that pervasive condition of
all experience and activity in which I formulate
intentions about what I shall do in the future, carry
them out in the present and remember them thereafter in
the past. Take away that understanding, and it might as
well be temperature that is signified by t.

Mellor denies this. He denies that anything ever
looks or sounds present, as opposed to past or future.
But some things look future: I duck and blink and flinch
as I perceive the approaching danger, and sigh with
relief when the dentist at last lays down the drill.
When I listen to Beethoven's Sixth Symphony, I hear the
future, the present and the past thunderstorm. Children,
long before they can tell the time, learn the meaning of
`later than' from their mother's `Not now, but when Daddy
comes home'. Mellor counters that the equivalence
between `later than' and `more future or less past'
cannot define `later than' because `later than' can also
be applied to tensed locations. But so what? Those who
adopt a tensed theory of time do not deny the value of
dates and other tenseless locutions. They would agree
with Mellor that tensed discourse was not independent of
tenseless discourse, though richer than it. We can give
an account of the future in terms of its being later than
the present, just as we can give an account of an event's
being later than now by use of the future tense. The
fact that we can do the former constitutes no reason for
claiming that the latter cannot be epistemically prior.

Arguments from meaning seldom are conclusive. The
second claim, that some token-reflexive term is needed to
secure reference, is more telling. Novels can be read
and understood, but are not literally true. Statements
purporting to be literally true need warranting, which
would be impossible if there were not token-reflexives to
point speaker and hearer, writer and reader, towards
relevant authorities and evidence. The English phrase
`Once upon a time' with its deliberate lack of temporal
reference indicates that the discourse is fictional.
Indeed, effective temporal reference seems a stronger
requirement than spatial or personal reference. My
intuition is that time is necessarily connected in a way
that space and persons are not. There is only one time,
whereas there could be two disconnected spaces (as in
Quinton's night-time dream world3) and there are many
societies with whose members we do not interact at all.
Unless I can date events I am talking about, I am only
telling tall tales. And to date an event is to use a
system in which we are able to locate ourselves: 1066 AD
dates the battle of Hastings only because we know that
now it is 1998 AD.

So token-reflexivity is not bad. But Mellor can
concede this, and still maintain that it is in some sense
unreal. Instead of Plato, he could appeal to the
authority of the Early Church, which laid down that the
mark of truth was that it was accepted semper, ubique and
ab omnibus. Or, more fashionably he could claim that the
methodology of physical science supported the view that
the real world is invariant over time, place and person,
and hence tenseless, spaceless, and impersonal. These
are, indeed, important marks of reality, but not the only
ones: as the argument of the previous paragraph shows,
extreme non-token-reflexivity lacks relevance for us. It
is not so much ``News from Nowhere'', as the
anti-Platonist gibe would have it, as not news at all, if it
has no bearing on us or our concerns. Only if at some
remove or other it tells us about us will it have any
bearing on our concerns. Just as a solipsistically
subjective account may be incommunicable, and certainly
is likely to lack interest for others, so a totally non-
token-reflexive, non-empirical account will equally lack
interest, and perhaps communicability, for everyone. An
adequate account must preserve the appearances, in order
that it may appear to us significant: and once experience
is recognised as relevant to reality, the near-universal
experience of the passage of time must be taken into
account. Even though the accounts given are often
metaphorical, widely understood metaphors are not to be
rubbished. We may be at a loss when someone speaks of
time having gone fast to answer the question ``How many
seconds a second?'', but this should be spur to think
more deeply rather than to dismiss the locution as
meaningless.

A determined projectivist might allow all that has
been argued in favour of token-reflexivity, and still
contend that tensed terms were imposed by us on the world
rather than discovered by us in the world. But the
testimony of modern physics, properly understood, refutes
that claim. Although the Special Theory of Relativity
has been thought by Mellor and others to tell against a
tensed theory,4
the arguments adduced are invalid, and in
any case countered by the General Theory. More
importantly, if we adopt a realist interpretation of
quantum mechanics, we are naturally led to seeing tense
as a fundamental feature of reality.

Several arguments have been based on the Special
Theory to support a ``block'' theory of the universe, and
hence tenseless time as an analogue to tenseless space.
Minkowski spacetime has encouraged people to think of
time as the fourth dimension, on a par with the three
dimension of space. But Minkowski spacetime is not a
simple four-dimensional space with four dimensions:
rather, it is one which has 3 + 1 dimensions with a
Lorentz signature that sharply distinguishes time-like
separations from space-like ones. The concept of
simultaneity has caused much confusion, particularly
``topological simultaneity'', which sounds like an
equivalence relation, but is not. Putnam and Rietdijk
have argued that two observers in two frames of reference
moving with a uniform velocity with respect to each other
will have different hyperplanes of simultaneity, and so
one event will be simultaneous with another which is
itself simultaneous with a third that is a causal
antecedent of the first: so it will be simultaneous with
an event that is absolutely earlier than it.5 But this
is a sophism, depending on our not noticing that
simultaneity in the Special Theory is, like other
equivalence relations, a triadic relation, in which two
things are equivalent to each other in respect of a third
feature that must itself be specified---in this case the
frame of reference. Simultaneity with respect to two
different frames of reference is not an equivalence
relation at all. If I was at the same school as you, and
you were at the same school as James, then whether it
follows that I was at the same school as James depends on
which school you shared with me and which with James. If
you were at the same nursery school as I was, and were at
Bristol Grammar School with James, nothing follows about
my having been at the same school as James.

A better argument is that an event future in one frame
of reference will be past with respect to another. So
whether an event is future or past depends on the choice
of a frame of reference, and cannot be anything absolute.
Nevertheless, that argument also fails. The hyperplanes
of simultaneity for a given frame of reference do not
determine what is currently going on at distant places,
but only what dates should be ascribed to them in order
to make electromagnetic phenomena coherent. As far as
electromagnetic phenomena are concerned, we have no means
of telling exactly when a distant event takes place; but
for any given frame of reference, IF we ascribe the same
date to all events on a particular hyperplane of
simultaneity, then Maxwell's equations apply neatly and
yield harmonious results. So far as the Special Theory
goes, simultaneity is a rather superficial and frame-
dependent property, which we find useful for assigning
dates to different events in different places, but which
is not of fundamental importance in accounting for the
propagation of causal influence. The ascription of
presentness, pastness, or futurity, to events outside the
light cone is nominal rather than real, and has no
bearing on their ontological status.6

Many physicists are persuaded by this argument. But
it is to lay too much weight on one physical theory. At
one time, perhaps, the Special Theory could claim to be
the last word in physics, and its principles to have
universal sway. From our vantage point its claims are
best evaluated by comparison with those of the Newtonian
system it supplanted. Although Newton believed in
absolute space, Newtonian mechanics could not, alone and
unaided, identify any frame of reference as being at rest
rather than in uniform motion. But, though by itself
relativistic as regards rest and uniform motion, it did
not rule out there being an absolute frame of reference--
-if the Michelson-Morley experiment had yielded a
positive result, we should have identified the rest frame
of the ether as being absolutely at rest. In the same
way, the Special Theory, though not itself picking out a
preferred frame of reference giving a world-wide
hyperplane of absolute simultaneity, does not rule it out
either. If, per impossibile, telepathic communications
were instantaneous, we should be able to identify a rest
frame in which the velocity of light was the same in all
directions and the hyperplane of simultaneity really did
pick out simultaneous events; we should do this, while
acknowledging the adequacy of other frames of reference
for dealing with electromagnetic phenomena, just as the
discovery of a rest frame for the ether would have still
allowed the adequacy of uniformly moving Galilean frames
for Newtonian mechanics. The Special Theory is not the
last word in physics, and its Principle of Equivalence
does not have to hold universally, and does not rule out
any preferred hyperplane of simultaneity. In fact, other
physical theories rule it in. Most cosmologists use a
version of the General Theory with boundary conditions
that determine a universe-wide world time. Admittedly,
cosmological theories are speculative, and liable to
change radically: but the mere fact that cosmologists at
present postulate a world time is enough to discredit
any argument from the Special Theory that there is
something unscientific in a world-wide hyperplane of
present simultaneity.

But physics goes further. It not only defeats the
would-be defeaters of the tense theory, but offers
positive support. Quantum mechanics, if it is to be
interpreted realistically, distinguishes a probabilistic
future of superimposed eigen-states from a definite past
in which each dynamical variable is in one definite
eigen-state, with the present being the moment at
which---to change the metaphor---the indeterminate ripple of
multitudinous wave-functions collapses into a single
definite wave. Admittedly, many of those who think about
quantum mechanics are not realists, and admittedly again,
there are horrendous difficulties in the way of giving a
coherent account of the collapse of the wave-function.
But an obstinate realism, as well as a slight sympathy
for our feline friends, precludes my envisaging any long
period in which Schr”dinger's cat could be half-dead and
half alive, and this whether she be in a laboratory in
Europe or on some planet circling Betelgeuse. There is a
definite fact of the matter, there as much as here,
whether or not we are dealing with a superposition of
functions or one definite eigen-function. And hence
there is a unique hyperplane advancing throughout the
whole universe of collapse into eigen-ness.

We can understand why philosophers have been led to
espouse a tenseless view of time, and also why they are
wrong to do so. Tenseless discourse leaves out too much.
It is difficult to see how I could acquire a specifically
temporal sense of temporal order without a tensed
understanding of time, any more than I could acquire a
full sense of personality without some first-personal
experience and agency. The austere intimations of
reality allowed by Plato are too austere: we cannot, on
pain of ultimate irrelevance, discount completely the
evidence of human experience, and the conditions in which
we are able to pool information and share rationality are
ones that ought to enter into any adequate account of
reality. The partial views of science, important and
illuminating though they are, are only partial views, and
the features they ignore do not on that account fail to
exist. It is too soon to suppose that quantum mechanics
is the last word in physics, or that the way it is
interpreted by me is the way it ought to be interpreted,
but at least at the present time it looks as if a tensed
view of time is in fact a view required not only by our
ordinary untutored experience, but as a fundamental
feature of the fabric of the physical universe.